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Robot Dynamics

How is the motion of a manipulator affected by external forces?
What joints torques are generated from external forces applied to the manipulator?
The following example will demonstrate how to calculate the joint torques required to counteract a given TCP wrench.

Create the Robot Model



In [1]:

    
from pybotics.robot import Robot
from pybotics.predefined_models import ur10

robot = Robot.from_parameters(ur10())

Define the Forces/Torques Acting on the TCP

Aka the "wrench"



In [2]:

    
forces = [0, 0, 10]
torques = [0, 0, 0]
wrench = [*forces, *torques]

Calculate Joint Torques

What are the joint torques required to counteract this payload?
This calculation can be repeated at each discrete pose in a trajectory for trajectory dynamics



In [5]:

    
import numpy as np

robot.joints = np.deg2rad([0, 0, 0, 0, 0, 0])
j_torques = robot.compute_joint_torques(wrench)
print(f'Robot Joints: {robot.joints}')
print(f'Joint Torques: {j_torques}')

robot.joints = np.deg2rad([0, -90, -90, 0, -90, 0])
j_torques = robot.compute_joint_torques(wrench)
print(f'Robot Joints: {robot.joints}')
print(f'Joint Torques: {j_torques}')









    



Robot Joints: [0. 0. 0. 0. 0. 0.]
Joint Torques: [11843.     0.     0.     0.     0.     0.]
Robot Joints: [ 0.         -1.57079633 -1.57079633  0.         -1.57079633  0.        ]
Joint Torques: [-1639.  7284.  1157.  1157.     0.     0.]